In this section we outline the mathematical framework for the spaces we are going to use. We recall from the literature the definition of ECT-spaces and we summarize some of their main properties.
We also discuss a particular subclass of ECT-spaces identified by linear differential operators with real constant coefficients that will be our target class for isogeometric analysis.
Afterwards, we introduce Tchebycheffian splines – piecewise functions where the pieces belong to given ECT-spaces glued together with certain smoothness – and we briefly discuss the construction of TB-splines, which are B-spline like basis functions for Tchebycheffian splines. We refer the reader to [1]}, [2]}, [3]}, [4]} for in-depth information about Tchebycheffian splines and spline functions in general.
